Remember: opposite (vertical) angles are equal, and adjacent angles that form a straight line add up to $180^\circ$. Which relationship connects the given $38^\circ$ angle to an obtuse angle?

Let $x$ be the measure of an obtuse angle. Write an equation that shows that $x$ and $38^\circ$ are supplementary (their sum is $180^\circ$), then solve for $x$.

In Desmos, type 180 - 38 and press Enter. The value that Desmos outputs is the measure, in degrees, of one of the obtuse angles formed with the $38^\circ$ acute angle.

When two straight lines cross, they form four angles:

• Opposite angles (vertical angles) are equal.
• Adjacent angles that form a straight line (a linear pair) are supplementary, meaning they add up to $180^\circ$.

So, every acute angle is adjacent to an obtuse angle, and those two must sum to $180^\circ$.

You are told that one of the acute angles measures $38^\circ$. The question asks for the measure of one of the obtuse angles.

Each obtuse angle is adjacent to this $38^\circ$ angle, so the acute angle and its neighboring obtuse angle form a straight line and must be supplementary.

Let $x$ be the measure of one obtuse angle.

Because the acute $38^\circ$ angle and the obtuse angle form a linear pair, their measures add to $180^\circ$:

Now solve for $x$ by subtracting $38^\circ$ from $180^\circ$:

Do the subtraction carefully.

Calculate the difference:

So, each obtuse angle formed by the intersection measures $142^\circ$, which corresponds to choice C.